Problem: Simplify the following expression: $z = \dfrac{r}{6} + \dfrac{r}{10}$
Answer: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $6$ and $10$ $\lcm(6, 10) = 30$ $ z = \dfrac{5}{5} \cdot \dfrac{r}{6} + \dfrac{3}{3} \cdot \dfrac{r}{10} $ $z = \dfrac{5r}{30} + \dfrac{3r}{30}$ $z = \dfrac{5r +3r}{30}$ $z = \dfrac{8r}{30}$ Simplify the expression by dividing the numerator and denominator by 2: $z = \dfrac{4r}{15}$